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QJEEAdv18Ma8879: JEE Advanced 2018 Mathematics - Class 12 JEEAdv18Ma8879 Solution

The value of ((log⁡29)2)1log⁡2(log⁡29)×(7)1log⁡47{({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}} is ....................

Step-by-Step Verified Solution

((log⁡29)2)1log⁡2(log⁡29)×(7)1log⁡47{({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}}

=(log⁡29)2.log⁡2log⁡29×712.log⁡74= {({\log _2}9)^{{{2.{{\log }_2}} \over {{{\log }_2}9}}}} \times {7^{{1 \over 2}.{{\log }_7}4}}

=(log⁡29)log⁡log⁡2922×7log⁡72= {({\log _2}9)^{{{\log }_{\log {2^{{9^{{2^2}}}}}}}}} \times {7^{{{\log }_7}2}}

=22×2=8= {2^2} \times 2 = 8

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